Substituting (REF ) in (REF ), the lower bound on the marginal log likelihood can be approximated as [1]}
\(p(\mathbf {y}|\Theta , \Omega , \bar{\Theta }) \ge  \mathcal {N} (\mathbf {0}, \mathbf {K}_{nm} \mathbf {K}^{-1}_{mm} \mathbf {K}_{nm}^\top + \sigma ^2_\epsilon \mathbf {I}) - {2} (\mathbf {K}_{nn} - \mathbf {Q}_{nn}).\) 
